Throttling for Zero Forcing and Variants

Joshua Carlson

Published 2018-07-18Version 1

Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertices that are initially blue and the number of time steps needed to color every vertex. We give a universal definition of throttling for variants of zero forcing and introduce the study of throttling for the minor monotone floor of zero forcing. For standard zero forcing and its floor, we characterize graphs with throttling number $\leq t$ as certain minors of cartesian products of complete graphs and paths. We apply these characterizations to power domination and extreme throttling numbers.